\(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)
\(=\left[\left(4x+1\right)\left(3x+2\right)\right]\left[\left(12x-1\right)\left(x+1\right)\right]-4\)
\(=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)
Đặt 12x2 + 11x -1 = a, ta được:
\(=\left(a+3\right)a-4\)
\(=a^2+3a-4\)
\(=a^2-a+4a-4\)
\(=a\left(a-1\right)+4\left(a-1\right)\)
\(=\left(a-1\right)\left(a+4\right)\)
\(=\left(12x^2+11x-1-1\right)\left(12x^2+11x-1+4\right)\)
\(=\left(12x^2+11x-2\right)\left(12x^2+11x+3\right)\)
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